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A080190
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Smallest prime p such that n applications of f lead form p to 2, where f is the mapping of primes > 2 to primes defined by A052248.
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1
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2, 3, 5, 7, 13, 23, 43, 83, 163, 317, 631, 1259, 2503, 5003, 9973, 19937, 39869, 119617, 239233, 480023, 960031, 1920049, 3840091, 7680181, 15360361, 30720719, 61441379, 122882741, 245765449, 491530873, 983061713, 1966123417
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OFFSET
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0,1
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COMMENTS
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RECORDS transform of A080189; prime p sets a new record for the number of applications of f that are required to reach 2. - a(n) = prime preceding 2*a(n-1) as long as a(n-1) is a term of A080191; if however a(n-1) is a term of A080192, then a(n) > 2*a(n-1). - Next term a(32) > 3932600000, presumably a(32) = 5274863189, a(33) = 10549726367. - The sequence coincides with A006992 (Bertrand primes: a(n) is largest prime < 2*a(n-1)) for the first 17 terms; first divergence occurs after term 39869 because this is the first term which belongs to A080192.
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LINKS
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FORMULA
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f^n(p) = 2.
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EXAMPLE
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f(23) = 13, f(13) = 7, f(7) = 5, f(5) = 3, f(3) = 2; five applications of f are required to reach 2 and for all primes < 23 at most four applications are required, so a(5) = 23.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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